Prism is a three-dimensional solid object in which the two ends are precisely the same shape. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms without the bases. If you take the cross-section of the prism parallel to its bases, the cross-sections will look like the bases. In this article, a complete explanation of the types, how to find the volume and area of a prism is given.
A prism has a solid shape consisting of two equal ends, flat faces or surfaces and identical cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve. Therefore, a prism can have cubic, rectangular, pentagonal and other polygon shapes but not the circular shape.
Types of Prism
Depending upon the cross-sections, the prisms are named. It is of two types, namely;
- Regular Prism
- Irregular Prism
If the bases of the prism are in the shape of a regular polygon, it is called regular prism.
If the bases are in the shape of an irregular polygon, then the prism is called an irregular prism.
Right Prism And Oblique Prism
Apart from regular and irregular, the prism can be classified into two more types;
- Right Prism
- Oblique Prism
The difference between both the prism are;
|Right Prism||Oblique Prism|
|If the faces and the joining edges are perpendicular to the base faces, then it is known as right prism||If the faces and the joining edges are not perpendicular to the base faces, then it is known as oblique prism|
|In a right prism, the side faces are rectangles||In an oblique prism, the side faces are parallelograms|
Based on the shape of the bases, it is further categorised into different types, namely;
- Triangular prism
- Square prism
- Rectangular prism
- Pentagonal prism
- Hexagonal prism
The formulas are defined for the surface area and volume of the prism. As the prism is a three-dimensional shape, so it has both the properties, i.e., surface area and volume.
Surface Area of a Prism
The surface area of the prism is the total area covered by the faces of the prism.
For any kind of prism, the surface area can be found using the formula;
Volume of a Prism
The volume of the prism is defined as the product of the base area and the prism height
For example, if you want to find the volume of a square prism, you must know the area of a square, then its volume can be calculated as follows:
The volume of a square Prism = Area of square×height
V = s2 × h cubic units
Where “s” is the side of a square.
Example 1: Find the volume of a triangular prism whose area is 60 cm2 and height is 7 cm.
Base area = 60 cm2
Height = 7 cm
We know that,
The volume of a prism = Base area × Height cubic units
Therefore, V = 60 ×7 = 420
Hence, the volume of a triangular prism = 420 cm3.
Example 2: Find the height of the square prism whose volume is 360 cm3 and the base area is 60 cm2.
The volume of a square prism = 360 cm3
Base Area = 60 cm2
Therefore, the height of the square prism is calculated as follows:
The volume of square prism = Base area × height
360 = 60 × prism height
Therefore, the height, h = 360/60
Prism Height, h = 6 cm.
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